Anthony served as churchwarden in the parish of Fordington, and signed the Bishops Transcripts in that office in 1623 and 1627. Having been an officer of his church, his motivation for emigration may have been more capitalist than religious. Antony Eames is listed as a passengers of the ship "Recovery of London", Gabriel Cornish, master, which sailed from Weymouth to New England on 16 Mar. 1633.[1]

Anthony received a grant of land in Hingham along with his son-in-law William Sprague in 1636, making him one of the original settlers of the area. Judging on the marriages of his children, he likely moved to Marshfield in the late 1650s.

Also called the "Recovery of London" and sometimes listed as a 1633 ship, as the list of passengers was erroneously dated 31 March 1633 instead of 1634. Many of its passengers briefly settled in Dorchester and were among the first settlers to Windsor, Connecticut in 1635.